Study of Temperature Stratification during Natural Convection of Gas in a Closed Volume

The article considers the problem of heat and mass transfer during natural convection of gas in a heated closed volume with an isothermal lower boundary in a mass force field. A simplified equation is proposed to describe heat transfer under temperature stratification conditions. For the problem of a free-convective boundary layer of a compressible gas on a plate under external temperature stratification conditions, analytical dependences for the velocity and temperature in the boundary layer are obtained. Good agreement is demonstrated between the analytical solutions for the boundary layer, the results of calculations using the stratification equation, and the simulation data of the full convection equations for the problem of heating of a vertical cylinder.